The reason I would want the TSN is to confirm that the unit does indeed have lifetime.

If buying a non-lifetimed unit, I might want to find out the account status to make sure that it conforms to what the seller is telling me.

For instance, if they said they discontinued the monthly sub half a year ago, but TiVo says it's an active account, that could be a red flag, and if the seller says he just paid for another month and TiVo says it's an inactive account, that's a red flag.

And of course if they say it's a a particular model, like say a TCD652160, and the TSN has a 540 in it instead of a 652, I know that the seller doesn't know what they're doing or they're trying to pull a fast one.